I found both the Phoa notes and the Jaap van Oosten book extremely helpful. The McLarty and the Freyd/Scedrov I like in general, but I didn’t find them especially useful in this particular connexion.
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Peter LeFanu LumsdaineFeb 19 '11 at 4:14

I think Freyd--Scedrov may be a good starting point for understanding the exact-completion construction of the effective topos, which is less often discussed than the tripos-to-topos version. Other good resources for this are the paper A categorical approach to realizability and polymorphic types by Carboni, Freyd and Scedrov, Carboni's Some free constructions in realizability and proof theory, and Robinson and Rosolini's Colimit completions and the effective topos.
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Finn LawlerFeb 19 '11 at 17:15

Andrew Pitts’ note “Tripos Theory in Retrospect” sheds some useful light on $\mathcal{Eff}$, from a slightly different angle than most other books do. It’s available at his publications page, and also at doi:10.1017/S096012950200364X (paywalled but potentially more durable).

For my part, even as quite a toposophile, $\mathcal{Eff}$ (and realizability toposes in general) took me a while to get comfortable with — a lot longer than any of the other genres, sheaves, syntactic ones, etc. In the end it must have taken about four or five attempts to get to grips with them, over several years — spending a little time getting a little way on each attempt, understanding one step in the construction (e.g.: the tripos-to-topos step in general), then waiting a few months while that sank in, before coming back for another crack at the next step. This certainly isn’t everyone’s experience, of course, but I’ve talked to at least a couple of other people who had a similar time.